Not quite so completely mental...
firemouth cichlids pair
bolivian rams pair
angel fish pair
neon tetras
rummynose tetras
tiger barbs
cories
red tail shark
gourami's
Yoyo loach
kuhli loach
Right, I think you may get away with the 3 pairs of cichlids if you are *very* lucky, best off choosing the Bolivian Rams and EITHER Angels or Firemouths. Maybe once tank is established you could try it, once you know your fishes personalities.
The neons are quite a small and slim bodied fish, will get eaten by both angels and firemouths... I would swap for a type of tetra thats much deeper in the body (rosy tetras, ornate tetras, black phantoms, red phantoms, flame tetra, harlequins etc) or better still, double up the size of the shoal of Rummynose, you will love the effect of having more!!
Tiger Barbs can be savage, you would need 15+ of them and even then, they will nip your angels and gouramis... How about thinking of a different species of barb? There are lots of great species that are less...well... psychotic... (Rhombo Barbs, Pentazonas,Parti Pentazonas, Cherry and Checkered to name a few!).
Corys are a gread idea! To be honest, choose a species you like and they will do great, 12-15 would be lovely, i would stick to one or two species as they do better in larger groups of each species and it means you might get babies
Red Tailed Shark... I dont know the excitement about these fish, i wish they werent even imported... they are thugs! They will cause havoc in the tank! You wont be able to mix them in with other territorial fishlike those cichlids and long finned gouramis and the shyer tetras. When you start adding fish that are going to cause a lot of stress into the tank, its going to stress fish out and you risk outbreaks of stress related/low immune system whitespot etc... He would also likely cause you problems with bottom dwellers like cories and loaches.
Goramis depends on which species! Avoid dwarf gouramis, too tempermental, easily stressed and prone to dying! If you stick with a pair/trio of Golds or opaline/three spots you will be ok or even better still Moonlight or Pearls (calmer species).
Yoyo loaches, nice to see its not clown loaches!! You will need to watch the Yoyos... as they get big they can get quite nippy too, some are ok, some i've seen go for angels... seems to vary... but atg about 16cm each i've seen these guys get big and boisterous! How about Botia Kubotai or a bigger group of the slightly smaller Botia Striata? Loaches in groups are great fun! Really active and encourages them to be out and about and doing the 'happy loach dance'.
And last but not least LOL khuli loach are neither here nor there, they are tiny and you very rarely see them (though good for eating left over foods).
If it was me, personally... it would be:
-Pair of Angels
-Pair of Bolivian Rams
-15-20 Rummynose
-10-15 Ornate Tetras
-15 sterbai corys (they are gorgeous and babies worth a bit)
-4 Pearl Gouramis (though might be tempted to swap for 6-8 Honey Gouramis)
-6 Botia Striata
Thats more than enough to be going on, by not having the shark, not having to have loads of tiger barbs, having two rather than three pairs of cichlids, it means you can up the shoals of smaller species quite nicely!
A lot of it will depend on decor too, lots of bogwood will keep the water nice and soft for your tetras and cichlids.
I might also add a pair of bristlenose to help eat algae...
And I would have to add loads of plants too
EDIT: Forgot to add, i would have super filtration and if after a year or so the tank is still doing great, i might add a shoal of Cherry barbs, they dont get big but really beautiful, personally i would just have a shoal of males as they make a far nicer display without the females in there.